Optimal Systems and Group Invariant Solutions for a Model Arising in Financial Mathematics

Abstract

Abstract. We consider a bond-pricing model described in terms of partial differential equations (PDEs). Classical Lie point symmetry analysis of the considered PDEs resulted in a number of point symmetries being admitted. The one-dimensional optimal system of subalgebras is constructed. Following the symmetry reductions, we determine the group-invariant solutions.

Lie Symmetries and Similarity transformations for the Generalized Boiti-Leon-Pempinelli equations

“…In this work we classify the admitted Lie point symmetries of the generalized BLP equations for various values of the free parameters n, m, while the latter are constrained by the theory of Lie symmetries. Such analysis is important for the detailed study of nonlinear partial differential equations and for the determination of new exact solutions, for other examples we refer the reader in [45,46,47,48] and references therein. The plan of the paper is as follows.…”

Optimal System, Invariant Solutions and Conservation Laws of the Dispersionless B type Kadomtsev-Petviashvili Equation

“…Hence, our study restricted with the vector fields Γ 1 to Γ 4 only. Now, using these vector fields, we construct the commutator table, the associated adjoint representation and one-dimensional optimal system [17,18,32,33,34,36,37,38,39,40,41] of (2.5), sufficient combination of vector fields (2.6). This allows us to find similarity transformations, reductions and exact solutions of (2.5).…”

Optimal System and Exact Solutions of Monge-Ampere Equation

“…In literature, there are many techniques available for obtaining optimal systems and a lot of excellent work has been done by experts e.g. [3,[5][6][7][8][9][10][11]13,18,[20][21][22][23]. Here, we use Peter J. Olver's technique [19] to derive optimal system for different cases of Monge-Ampere equation by assuming different particular values of the non-homogeneous part f (x, y).…”